4. A computer seller has three brands of computers. Out of...

4. A computer seller has three brands of computers. Out of the all computers he sells, 50% are brand 1, 30% are brand 2, and the rest is brand 3. By his experience, he knows that out of brand 1, 1% computers are returned. These percentages for brands 2 and 3 are 2% and 1.5%, respectively. a) What is the probability that a customer will return a computer? b) If a customer has returned a computer, what is the probability that is a not a brand 3?

Transcript

00:01 In question 4, the probability of brand 1 computer is given as 50 percentage which is equal to 0 .50 and the probability of brand 2 computer is given as 30 percentage which will be equal to 0 .30.

00:23 Now we have to find the probability of brand 3 computer.

00:30 We know that sum of probabilities will be equal to 1.

00:35 Thus the probability of brand 3 computer will be equal to 1 minus probability of brand 1 computer plus probability of brand 2 computer, which is 1 minus 0 .50 plus 0 .50 plus 0 .3.

00:53 Which is 1 minus 0 .80 which is 0 .20.

01:01 Thus the probability of brand 3 computer is 0 .20 and it is also given that the probability of repair given it is the brand 1 computer is given as 1 percentage which will be equal to 0 .01 and the probability that the probability that the computer will be written given that it is a brand to computer is given us 2 percentage which will be equal to 0 .02 and the probability that the computer will be written given that it is of the third brand is given us 1 .5 percentage which will be equal to 0 .015.

01:50 Now in part a we have to find the probability that the computer will be returned and which is calculated as probability that are given 1 into probability of brand 1 computer plus probability of are given brand 2 into probability of brand 2 computer plus probability of are given 3 into probability of brand 3 computer now substituting the values would give 0 .01 into 0 .50 plus 0 .0 .02 into 0 .30 plus 0 .30 plus 0 .0 .30 plus 0 .0 .0 .30 plus 0.

02:40 15 into 0 .20.

02:44 Now simplifying this gives 0 .005 plus 0 .006 plus 0 .03.

02:55 Thus, simplifying this would give 0 .014.

03:00 Thus, the probability that the computer will be written as 0 .014...

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